Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-2y &= 1 \\ 7x+9y &= 3\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $7x = -9y+3$ Divide both sides by $7$ to isolate $x$ $x = {-\dfrac{9}{7}y + \dfrac{3}{7}}$ Substitute this expression for $x$ in the first equation. $-({-\dfrac{9}{7}y + \dfrac{3}{7}}) - 2y = 1$ $\dfrac{9}{7}y - \dfrac{3}{7} - 2y = 1$ Simplify by combining terms, then solve for $y$ $-\dfrac{5}{7}y - \dfrac{3}{7} = 1$ $-\dfrac{5}{7}y = \dfrac{10}{7}$ $y = -2$ Substitute $-2$ for $y$ in the top equation. $-x-2( -2) = 1$ $-x+4 = 1$ $-x = -3$ $x = 3$ The solution is $\enspace x = 3, \enspace y = -2$.